Timoshenko - Theory of Plates & Shells
Timoshenko - Theory of Plates & Shells
(OP)
2nd Edition, Chapter 1, Article 1 the following statement is made and is key to the solution: "The lateral strain in the y direction must be zero in order to maintain continuity in the plate during bending..."
I don't grasp that concept. It seems to me like there could be a small amount of strain in the y direction, and rather than a loss of continuity, the cross section of the plate would end up as a trapezoid.
What am I missing?
Thanks in advance!
I don't grasp that concept. It seems to me like there could be a small amount of strain in the y direction, and rather than a loss of continuity, the cross section of the plate would end up as a trapezoid.
What am I missing?
Thanks in advance!





RE: Timoshenko - Theory of Plates & Shells
Cheers
Greg Locock
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RE: Timoshenko - Theory of Plates & Shells
That statement is a simplification, an idealized condition, but pretty close to the truth vs. the real world or exact condition, and for a long or infinitely long plate; so that a strip of unit width can be used and analyzed as representing a typical strip anywhere in the plate length, removed from too near the ends of the plate or reaction locations. This simplification is akin to the simplification Timoshenko makes when talking about ‘Plane Stress’ and ‘Plane Strain,’ in chap. 2 of his “Theory of Elasticity” text. This was pretty much a basic assumption, a first step, in simplifying many of our daily engineering analysis problems, until we really do start thinking three dimensionally about a volume of material under load.
RE: Timoshenko - Theory of Plates & Shells
Thanks for the reply. I guess that make sense. Just for fun I decided to run the math using the assumption that the stress in the y direction was 0. No surprise here, but I ended up with EI(d2w/dx2) = -M. So I guess the width of the plate makes the zero y-strain a more appropriate simplification than a zero y-stress simplification.
Greg, I don't know what you mean by your question exactly.
RE: Timoshenko - Theory of Plates & Shells
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Timoshenko - Theory of Plates & Shells
RE: Timoshenko - Theory of Plates & Shells
If you have a beam, you assume zero stress in the Y-direction and whatever strain occurs, there it is- the comopression flange can get wider and the tension flange can get narrower when bent. With a wide plate or wide bar, the compression and tension faces are tied together and can't move sideways relative to each other, so you assume zero strain rather than zero stress.
When I was in college in an ME lab, we did a strain-gauge test of a beam, which was a flat bar about an inch wide and 1/8" thick. Our strains were off somewhat from what they should have been, and it was only years later, I figured out why- from this effect. I believe Roark mentions it in connection with flat bars bent the easy way.
RE: Timoshenko - Theory of Plates & Shells
RE: Timoshenko - Theory of Plates & Shells
And now that I think about it, maybe we were measuring deflection of the beam, rather than strain with strain gauges- it's been a while.
RE: Timoshenko - Theory of Plates & Shells
http://www.eng-tips.com/viewthread.cfm?qid=413308
RE: Timoshenko - Theory of Plates & Shells
RE: Timoshenko - Theory of Plates & Shells
(joke stolen shamelessly from Greg)
RE: Timoshenko - Theory of Plates & Shells
RE: Timoshenko - Theory of Plates & Shells
A quick google found this link. http://155.207.34.6/files/Timoshenko.pdf
Some light beach reading.
RE: Timoshenko - Theory of Plates & Shells
RE: Timoshenko - Theory of Plates & Shells
RE: Timoshenko - Theory of Plates & Shells
RE: Timoshenko - Theory of Plates & Shells
Russian born Stephen P. Timoshenko is widely considered to be the father of Engineering Mechanics
https://en.wikipedia.org/wiki/Stephen_Timoshenko
MJCronin
Sr. Process Engineer
RE: Timoshenko - Theory of Plates & Shells
I appreciate your response, but in the text the plate thickness is in the z-direction. The unloaded plate is in the xy-plane.
RE: Timoshenko - Theory of Plates & Shells
One implicit assumption of the analysis model of taking one strip of the plate as independent beam is the plate dimension along y direction is far larger than those in both x and z directions. The plane strain theory is applicable in this case and therefore the strain along y direction is zero.
RE: Timoshenko - Theory of Plates & Shells